A265200 Numbers n such that n!3 + 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

8, 10, 11, 13, 16, 19, 20, 22, 37, 38, 47, 73, 92, 94, 100, 218, 241, 284, 482, 541, 736, 787, 829, 916, 1147, 1312, 1856, 1928, 2035, 3134, 4958, 5503, 8042, 16898, 16987, 24548, 25076, 35086

Offset

1,1

Comments

Corresponding primes are: 2267, 2467, 3067, 5827, 60427, 1108747, 4190987, 24346507, 664565853954187, ...

a(39) > 50000.

Terms > 38 correspond to probable primes.

Links

Table of n, a(n) for n=1..38.

Henri & Renaud Lifchitz, PRP Records. Search for n!3+2187.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

11!3 + 3^7 = 11*8*5*2 + 2187 = 3067 is prime, so 11 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^7] &]
Select[Range[35100], PrimeQ[Times@@Range[#, 1, -3]+2187]&] (* Harvey P. Dale, Oct 19 2023 *)

Prog

(PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^7), print1(n , ", "))) \\ Altug Alkan, Dec 04 2015

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994, A261145.

Sequence in context: A242857 A031037 A006757 * A126803 A256385 A274560

Adjacent sequences: A265197 A265198 A265199 * A265201 A265202 A265203

Keyword

nonn,more

Author

Robert Price, Dec 04 2015

Status

approved